Lenses and Waves

Chapter 1
Introduction – ‘the perfect Cartesian’
Christiaan Huygens, optics & the scientific revolution
“EYPHKA. The confirmation of my theory of light and refractions”,
proclaimed Christiaan Huygens on 6 August 1679. The line is accompanied
by a small sketch, consisting of a parallelogram, an ellipse (though barely
recognizable as such) and two pairs of perpendicular lines (Figure 1). The
composition of geometrical figures does not immediately divulge its
meaning. Yet, it conveys a pivotal event in the development of seventeenthcentury
science.
What is it? The parallelogram is a
section – the principal section – of a piece
of Iceland crystal, which is a transparent
form of calcite with extraordinary optical
properties. It refracts rays of light in a
strange way that does not conform to the
established laws of refraction. The ellipse
represents the propagation of a wave of
light in this crystal. It is not an ordinary,
spherical wave, as waves of light are by
Figure 1 The sketch of 6 August 1679
nature, but that is precisely because the elliptical shape explains the strange
refraction of light rays in Iceland crystal. The two pairs of lines denote the
occasion for Huygens’ joy. They are unnatural sections of the crystal, which
he had managed to produce by cutting and polishing the crystal. They
produced refractions exactly as his theory, by means of those elliptical waves,
had predicted.
The elliptical waves were derived from the wave theory he had developed
two years earlier, with the formulation of a principle of wave propagation.
Like ordinary spherical waves, these elliptical waves were hypothetical
entities defining the mechanistic nature of light. Now, seventeenth-century
science was full of hypotheses regarding the corpuscular nature of things.
But Huygens’ wave theory was not just another corpuscular theory. His
principle defined the behavior of waves in a mathematical way, based on a
theory describing the mechanics of light propagation in the form of
collisions between ether particles. The mathematical character of Huygens’
wave theory is historically significant. Huygens was the first in the
seventeenth century to fully mathematize a mechanistic explanation of the
properties of light. As contrasted to the qualitative pictures of his
contemporaries, he could derive the exact properties of rays refracted by